Observed log-chlorophyll at representative station in SF Bay Delta region.
library(tidyverse)
library(lubridate)
library(mgcv)
library(plotly)
library(WRTDStidal)
library(gridExtra)
source('R/funcs.R')
# flow data, left moving window average of 30 days
data(sf_fldat)
fl_dat <- sf_fldat %>%
rename(date = Date) %>%
filter(station %in% 'sac') %>%
mutate(
qsm = stats::filter(q, rep(1, 30)/30, sides = 1, method = 'convolution')
)
# format the data to model
data(sf_dat)
sf_mod <- sf_dat %>%
filter(Site_Code %in% 'C3') %>%
rename(date = Date) %>%
mutate(
doy = yday(date),
dec_time = decimal_date(date),
yr = year(date),
mo = month(date, label = T)
) %>%
left_join(fl_dat, by = 'date') %>%
mutate(
flo = log(qsm),
lnchl = log(chl)
) %>%
select(-q, -qsm, -station, -Latitude, -Longitude, -Location)
# plot, all
p <- ggplot(sf_mod, aes(x = date, y = lnchl)) +
geom_line() +
theme_bw()
ggplotly(p)
# boxplot, by years
p <- ggplot(sf_mod, aes(x = yr, y = lnchl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)
# boxplot, by month
p <- ggplot(sf_mod, aes(x = mo, y = lnchl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)
Some simple GAMs to explore annual, seasonal trends.
# smooths to evaluate
smths <- c(
"s(dec_time, bs = 'tp')",
"s(doy, bs = 'cc')",
"te(dec_time, doy, bs = c('tp', 'cc'))"
)
# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
frm <- combn(smths, i) %>%
apply(2, function(x){
paste(x, collapse = ' + ') %>%
paste('lnchl ~ ', .) %>%
formula
})
frms <- c(frms, frm)
}
# create models from smooth formula combinations
mods <- map(frms, function(frm){
gam(frm,
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
})
names(mods) <- paste0('mod', seq_along(mods))
Summary stats of annual, seasonal models:
# smoother stats of GAMs
map(mods, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable
| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| mod1 | s(dec_time) | 6.866894 | 7.962040 | 29.957511 | 0.0000000 |
| mod2 | s(doy) | 3.191626 | 8.000000 | 12.600387 | 0.0000000 |
| mod3 | te(dec_time,doy) | 13.362860 | 15.974582 | 27.262699 | 0.0000000 |
| mod4 | s(dec_time) | 7.272455 | 8.281637 | 35.566876 | 0.0000000 |
| mod4 | s(doy) | 3.591968 | 8.000000 | 18.279046 | 0.0000000 |
| mod5 | s(dec_time) | 7.347362 | 8.329118 | 18.745688 | 0.0000000 |
| mod5 | te(dec_time,doy) | 8.792719 | 15.000000 | 11.089349 | 0.0000000 |
| mod6 | s(doy) | 2.933188 | 8.000000 | 2.355489 | 0.0000000 |
| mod6 | te(dec_time,doy) | 10.642911 | 12.982207 | 22.279284 | 0.0000000 |
| mod7 | s(dec_time) | 7.332864 | 8.308760 | 9.278011 | 0.0000000 |
| mod7 | s(doy) | 3.385611 | 8.000000 | 5.284500 | 0.0000000 |
| mod7 | te(dec_time,doy) | 6.637691 | 15.000000 | 1.417708 | 0.0003557 |
# summary stats of GAMs
map(mods, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable
| name | AIC | R2 |
|---|---|---|
| mod1 | 1117.9219 | 0.3025777 |
| mod2 | 1215.8161 | 0.1606211 |
| mod3 | 995.0956 | 0.4490483 |
| mod4 | 986.8771 | 0.4548302 |
| mod5 | 972.2099 | 0.4741757 |
| mod6 | 992.1514 | 0.4522078 |
| mod7 | 971.9230 | 0.4755770 |
# prediction data
pred_dat <- data.frame(
dec_time = seq(min(sf_mod$dec_time), max(sf_mod$dec_time), length = 1000)
) %>%
mutate(
date = date_decimal(dec_time),
date = as.Date(date),
mo = month(date, label = TRUE),
doy = yday(date),
yr = year(date)
) %>%
left_join(., fl_dat[, c('date', 'qsm')]) %>%
mutate(flo = log(qsm)) %>%
select(-qsm)
# predictions
sf_res <- map(mods, function(x){
pred_dat %>%
mutate(
pred = predict(x, newdata = pred_dat)
)
}) %>%
enframe('mods') %>%
unnest
# plot
p <- ggplot(sf_res, aes(x = date)) +
geom_point(data = sf_mod, aes(y = lnchl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)
# plot
p <- ggplot(sf_res, aes(x = doy, group = factor(yr), colour = yr)) +
geom_line(aes(y = pred)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
) +
facet_wrap(~ mods, ncol = 2)
ggplotly(p)
Adding flow data to the model:
# smooths to evaluate
smths <- c(
"s(dec_time, bs = 'tp')",
"s(doy, bs = 'cc')",
"s(flo, bs = 'tp')",
"te(flo, doy, bs = c('tp', 'cc'))",
"te(flo, dec_time, bs = c('tp', 'tp'))",
"te(dec_time, doy, bs = c('tp', 'cc'))",
"te(dec_time, doy, flo, bs = c('tp', 'cc', 'tp'))"
)
# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
frm <- combn(smths, i) %>%
apply(2, function(x){
paste(x, collapse = ' + ') %>%
paste('lnchl ~ ', .) %>%
formula
})
frms <- c(frms, frm)
}
# create models from smooth formula combinations
mods2 <- map(frms, function(frm){
gam(frm,
knots = list(doy = c(1, 366)),
data = sf_mod,
na.action = na.exclude
)
})
names(mods2) <- paste0('mod', seq_along(mods2))
Summary stats of best year/season model, year/season/flow model
# best model with only season, year
best1 <- map(mods, AIC) %>%
unlist %>%
which.min %>%
mods[[.]]
# best model with season, year, flow
best2 <- map(mods2, AIC) %>%
unlist %>%
which.min %>%
mods2[[.]]
best <- list(best1 = best1, best2 = best2)
# smoother stats of GAMs
map(best, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable
| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| best1 | s(dec_time) | 7.332864 | 8.308760 | 9.2780106 | 0.0000000 |
| best1 | s(doy) | 3.385611 | 8.000000 | 5.2844996 | 0.0000000 |
| best1 | te(dec_time,doy) | 6.637691 | 15.000000 | 1.4177080 | 0.0003557 |
| best2 | s(dec_time) | 6.587614 | 7.657166 | 8.8044126 | 0.0000000 |
| best2 | s(doy) | 3.262079 | 8.000000 | 1.1046635 | 0.0010105 |
| best2 | te(flo,dec_time) | 10.316629 | 20.000000 | 3.8902702 | 0.0000000 |
| best2 | te(dec_time,doy) | 8.322306 | 15.000000 | 2.1431672 | 0.0000026 |
| best2 | te(dec_time,doy,flo) | 8.912490 | 32.000000 | 0.9655715 | 0.0000223 |
# summary stats of GAMs
map(best, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable
| name | AIC | R2 |
|---|---|---|
| best1 | 971.9230 | 0.4755770 |
| best2 | 869.6463 | 0.5796506 |
# predictions
sf_res2 <- map(best, function(x){
pred_dat %>%
mutate(
pred = predict(x, newdata = pred_dat)
)
}) %>%
enframe('mods') %>%
unnest
# plot
p <- ggplot(sf_res2, aes(x = date)) +
geom_point(data = sf_mod, aes(y = lnchl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)
ptheme <- theme(
axis.title.x = element_blank(),
axis.title.y = element_blank()
)
cols <- 'Spectral'
pb1 <- dynagam(best1, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('Best 1')
pb2 <- dynagam(best2, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
ggtitle('Best2')
pleg <- g_legend(pb2)
pb2 <- pb2 +
theme(legend.position = 'none')
grid.arrange(
pleg,
arrangeGrob(pb1, pb2, ncol = 2, bottom = 'lnQ', left = 'lnchl'),
ncol = 1,
heights = c(0.1, 1)
)